Optimal control of wind farm power output with delay compensated nested-loop extreme seeking control

In this paper, we propose to enhance the nested-loop extremum seeking control (NLESC)-based wind farm control strategy with the predictor-based delay compensation in order to improve its convergence characteristics under fluctuating wind. Earlier work has shown the effectiveness of NLESC for region-2 wind farm operation, i.e., maximizing the total power output of cascaded wind turbine array, while its convergence speed is highly limited by the delay of power output for downstream turbines due to wake propagation along the wind direction. By utilizing the delay compensated ESC proposed by Oliveira and Krstic, the delay compensated NLESC (DCNLESC) wind farm control is proposed, allowing the dither frequencies to be of similar magnitude as that in the single-turbine ESC. This can significantly improve the convergence speed of optimum tracking for real-time wind farm control. The wake propagation delay is estimated from turbine power outputs using cross correlation and proper filtering. Using the SimWindFarm platform, the proposed DCNLESC strategy is simulated with both a single-column three-turbine array and a 2 × 3 turbine array, under different wind speeds. The results show that the convergence speed toward the calibrated optimum is significantly improved over the NLESC operation. The convergence time for the upstream turbines' torque gain is reduced by 55%–14% in terms of integral time-weighted absolute error, while the impact on turbine fatigue loads is as low as no more than 3.5% increase on turbine tower and shaft.